Algorithm for multiple-symbol differential detection

ABSTRACT

A method for differential phase evaluation of M-ary communication data is employed in which the data consists of N sequential symbols r 1  . . . r N , each having one of M transmitted phases. Selected sequences of N−1 elements that represent possible sequences of phase differentials are evaluated using multiple-symbol differential detection. Using r 1  as the reference for each phase differential estimate, s N−1  phase differential sequences are selected in the form (P 2i , P 3i , . . . , P Ni ) for i=1 to s for evaluating said symbol set, where s is predetermined and 1&lt;s&lt;M. Each set of s phase differential estimate values are chosen based on being the closest in value to the actual transmitted phase differential value. These s phase differential estimates can be determined mathematically as those which produce the maximum results using conventional differential detection.

FIELD OF THE INVENTION

[0001] This invention relates to differential detection ofmultiple-phase shift keying (MPSK) modulation in communication systems.This invention generally relates to digital communications, including,but not limited to CDMA systems.

BACKGROUND OF THE INVENTION

[0002] Conventionally, communication receivers use two types of MPSKmodulated signal detection: coherent detection and differentialdetection. In coherent detection, a carrier phase reference is detectedat the receiver, against which subsequent symbol phases are compared toestimate the actual information phase. Differential detection processesthe difference between the received phases of two consecutive symbols todetermine the actual phase. The reference phase is the phase of thefirst of the two consecutive symbols, against which the difference istaken. Although differential detection eliminates the need for carrierphase reference processing in the receiver, it requires a highersignal-to-noise ratio at a given symbol error rate.

[0003] Differential detection in an Additive White Gaussian Noise (AWGN)channel is preferred over coherent detection when simplicity ofimplementation and robustness take precedence over receiver sensitivityperformance. Differential detection is also preferred when it isdifficult to generate a coherent demodulation reference signal. Fordifferential detection of multiple-phase shift keying (MPSK) modulation,the input phase information is differentially encoded at thetransmitter, then demodulation is implemented by comparing the receivedphase between consecutive symbol intervals. Therefore, for properoperation, the received carrier reference phase should be constant overat least two symbol intervals.

[0004] Multiple-symbol differential detection (MSDD) uses more than twoconsecutive symbols and can provide better error rate performance thanconventional differential detection (DD) using only two consecutivesymbols. As in the case of DD, MSDD requires that the received carrierreference phase be constant over the consecutive symbol intervals usedin the process.

[0005] Detailed discussions of MSDD and Multiple Symbol Detection (MSD)are found in, “Multiple-Symbol Differential Detection of MPSK” (Divsalaret al., IEEE TRANSACTIONS ON COMMUNICATIONS, Vol. 38, No. 3, March 1990)and “Multiple-Symbol Detection for Orthogonal Modulation in CDMA System”(Li et al., IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, Vol. 50, No. 1,January 2001).

[0006] Conventional MPSK MSDD is explained in conjunction with FIGS. 1and 2 below. FIG. 1 shows an AWGN communication channel 101 with an MPSKsignal sequence r that comprises N consecutive symbols r₁ . . . r_(N)received by receiver 110. Symbol r_(k) represents the k^(th) componentof the N length sequence r, where 1≦k≦N. The value for r_(k) is a vectorrepresented by Equation (1): $\begin{matrix}{r_{k} = {{\sqrt{\frac{2E_{s}}{T_{s}}}^{{j\varphi}_{k} + {j\theta}_{k}}} + n_{k}}} & {{Eq}.\quad (1)}\end{matrix}$

[0007] having symbol energy E_(S), symbol interval T_(S) and transmittedphase φ_(k) where j={square root}{square root over (−1)}. Value n_(k) isa sample taken from a stationary complex white Gaussian noise processwith zero mean. Value θ_(k) is an arbitrary random channel phase shiftintroduced by the channel and is assumed to be uniformly distributed inthe interval (−π, π). Although channel phase shift θ_(k) is unknown,differential detection conventionally operates assuming θ_(k) isconstant across the interval of observed symbols r₁ to r_(N). Fordifferential MPSK (DMPSK), phase information is differentially encodedat the transmitter, and transmitted phase φ_(k) is represented by:

φ_(k)=φ_(k−1)+Δφ_(k)  Eq. (2)

[0008] where Δφ_(k) is the transmitted information phase differentialcorresponding to the k^(th) transmission interval that takes on one of Muniformly distributed values within the set Ω={2 πm/M, m=0, 1, . . . ,M−1} around the unit circle, as in a Gray mapping scheme. For example,for QPSK, M=4 and Δφ_(k)=0, π/2, π, or 3π/2 for each k from 1 to N.

[0009] It is assumed for simplicity that arbitrary phase value θ_(k) isconstant (θ_(k) =θ) over the N-length of the observed sequence.

[0010] At the receiver, optimum detection using multiple-symboldifferential detection (MSDD) is achieved by selecting an estimatedsequence of phase differentials {d{circumflex over (φ)}₁, d{circumflexover (φ)}₂, . . . , d{circumflex over (φ)}_(N−1)} which maximizes thefollowing decision statistic: $\begin{matrix}{\eta = {\max\limits_{{d\quad {\hat{\varphi}}_{1}},{d\quad {\hat{\varphi}}_{2}},\quad \ldots \quad,{{d\quad {\hat{\varphi}}_{N - 1}} \in \Omega}}{{r_{1} + {\sum\limits_{m = 2}^{N}{r_{m}^{{- j}\quad d\quad {\hat{\varphi}}_{m - 1}}}}}}^{2}}} & {{Eq}.\quad (3)}\end{matrix}$

[0011] By Equation (3), the received signal is observed over N symboltime intervals while simultaneously selecting the optimum estimatedphase sequence {d{circumflex over (φ)}₁, d{circumflex over (φ)}₂, . . ., d{circumflex over (φ)}_(N−1)}. The maximized vector sum of theN-length signal sequence r_(k), provides the maximum-likelihooddetection, where estimated phase differential d{circumflex over (φ)}_(m)is the difference between estimated phase {circumflex over (φ)}_(m+1)and the estimate of the first phases {circumflex over (φ)}.

d{circumflex over (φ)}_(m)={circumflex over (φ)}_(m+1)−{circumflex over(φ)}₁.  Eq.(4)

[0012] The estimate of transmitted information phase sequence{Δ{circumflex over (φ)}₁, Δ{circumflex over (φ)}₂, . . . , Δ{circumflexover (φ)}_(N−1)} is obtained from the estimated phase sequence{d{circumflex over (φ)}₁, d{circumflex over (φ)}₂, . . . , d{circumflexover (φ)}_(N−1)} using Equation (5). $\begin{matrix}{{d\quad {\hat{\varphi}}_{m}} = {\sum\limits_{k = 1}^{m}{\Delta \quad {\hat{\varphi}}_{k}}}} & {{Eq}.\quad (5)}\end{matrix}$

[0013] Value Δ{circumflex over (φ)}_(k) is an estimate of transmittedphase differential Δφ_(k). Since d{circumflex over (φ)}_(k) (1≦k≦N−1)takes on one of M uniformly distributed Ω values {2 πm/M, m=0, 1, . . ., M−1}, the conventional MSDD detection searches all possible phasedifferential sequences and there are M^(N−1) such phases. The error rateperformance improves by increasing the observed sequence length N, whichpreferably is selected to be N=4 or N=5. As an example, for 16 PSKmodulation with N=5, the number of phase differential sequences tosearch is 16⁴=65536. As evident by this considerably large number ofsequences, simplicity in the search sequence is sacrificed in order toachieve a desirable error rate performance.

[0014]FIG. 2 shows the process flow diagram for algorithm 200, whichperforms conventional MSDD. It begins with step 201 where N consecutivesymbols r_(k) for k=1 to N are observed. Next, the possible sets ofphase differential sequences {d{circumflex over (φ)}₁, d{circumflex over(φ)}₂, . . . , d{circumflex over (φ)}_(N−1)} where each d{circumflexover (φ)}_(k), for k=1 to N−1, is one from the set of M uniformlydistributed phase values in the set Ω={2 πm/M, m=0, 1, . . . , M−1}.There are M^(N−1) possible sets. FIG. 5 shows an example of an array ofsuch sets, where N=4 and M=4, which illustrates the 4⁴⁻¹=64 possiblesets of phase differential sequences. In step 203, each possible phasesequence is attempted in the expression${{r_{1} + {\sum\limits_{m = 2}^{N}{r_{m}^{{- j}\quad d\quad {\hat{\varphi}}_{m - 1}}}}}}^{2}\quad,$

[0015] giving a total of M^(N−1) values. Next, in step 204, the maximumvalue is found for step 203, which indicates the best estimate phasedifferential sequence. Finally, in step 205, the final information phasesequence {Δ{circumflex over (φ)}₁, Δ{circumflex over (φ)}₂, . . . ,Δ{circumflex over (φ)}_(N−1)} is estimated from {d{circumflex over(φ)}₁, d{circumflex over (φ)}₂, . . . , d{circumflex over (φ)}_(N−1)}using Equation (5) and the information bits are obtained from Grayde-mapping between phase and bits.

[0016] Although MSDD provides much better error performance thanconventional DD (symbol-by-symbol), MSDD complexity is significantlygreater. Therefore, it is desirable to provide an improved method andsystem for MSDD with less complexity.

SUMMARY

[0017] A method for multiple-symbol differential detection phaseevaluation of M-ary communication data is employed in which the dataconsists of N sequential symbols r₁ . . . r_(N), each having one of Mtransmitted phases. Selected sequences of N−1 elements that representpossible sequences of phase differentials are evaluated usingmultiple-symbol differential detection. Next, using r₁ as the referencefor each phase differential estimate, s^(N−1) phase differentialsequences are selected in the form (P_(2i), P_(3i), . . . , P_(Ni)) fori=1 to s for evaluating said symbol set, where s is predetermined and1<s<M. Rather than attempting every one of the M possible phasedifferential values during the estimation, the reduced subset of s phasedifferential estimate values are chosen based on being the closest invalue to the actual transmitted phase differential value. These s phasedifferential estimates can be determined mathematically as those whichproduce the maximum results in the differential detection expression|r₁+r_(k+1)e^(−jβ) ^(_(k)) |².

[0018] Each of the s^(N−1) phase differential sequences are thenevaluated using MSDD to determine the final maximum likelihood phasesequence. The resulting final phase sequence can be used to determinethe information phase estimates and the phase information bits by Grayde-mapping.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019]FIG. 1 shows a representation of a channel symbol stream for areceiver.

[0020]FIG. 2 shows a process flow diagram of an algorithm 200 forconventional MSDD.

[0021]FIG. 3A shows a process flow diagram of an algorithm 300 forreduced complexity MSDD.

[0022]FIG. 3B shows a detailed process flow diagram for step 302 of FIG.3A.

[0023]FIGS. 4A, 4B, 4C show a block diagram of an implementation of thereduced complexity MSDD algorithm.

[0024]FIG. 5 shows a table of possible phase sequences processed by aconventional MSDD algorithm.

[0025]FIG. 6 graphically shows a comparison of the symbol error rateperformances for the conventional and simplified MSDD algorithms.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026]FIG. 3A shows a MSDD algorithm 300 that reduces the searchcomplexity of the MSDD of algorithm 200, using a subset search concept.First, in step 301, N consecutive symbols r_(k) are observed for1≦k≦N−1. In step 302, s^(N−1) sets of phase differential estimatesequences {β₁, β₂, . . . , β_(N−1) } are selected as optimum estimatesfrom among the full set of M^(N−1) phase estimates attempted inalgorithm 200. Turning to FIG. 3B, step 302 is broken down in furtherdetail. In step 302A, the initial received signal r₁ is selected as apreferred reference for determining phase differentials between r₁ andeach subsequent r_(k). In step 302B, a small candidate subset of s phasedifferential estimates {β_(k1), β_(k2), . . . , β_(ks)}(1≦k ≦N−1), amongall M possible phases {2 πm/M, m=0, 1, . . . , M−1 } where 1<s<M and sis predetermined. The s phase estimates that are selected are theclosest in value to the actual phase differential Δφ_(k). In order toobtain the closest values for the phase differential estimates, eachβ_(k) is applied to the conventional DD expression |r₁ +r_(k+1) e^(−jβ)^(_(k)) |² from which the s phase differential estimates {β_(k1),β_(k2), . . . , β_(ks) } that produce the maximum resulting value areselected. With the inclusion of this symbol-by-symbol DD process step(302B), it can be seen that algorithm 300 is a combination of MSDD andDD processing. In step 302C, there are now s^(N−1) sets of optimum phasedifferential sequences, where P_(k)={β_(k1), β_(k2), . . . , β_(ks)}.Returning to FIG. 3A, the result of step 302 is s^(N−1) sequences ofphases (P₁, P₂, . . . P_(N−1)). These are the maximum-likelihood phasedifferential candidates. That is, the s values for P₁ are the closest invalue to the actual phase differential Δφ₁, the s values for P₂ are theclosest to actual phase differential Δφ₂, and so on.

[0027] In step 303, all s^(N−1) possible phase sequences (P₁, P₂, . . .P_(N−1)) are attempted within the expression${{r_{1} + {\sum\limits_{m = 2}^{N}{r_{m}^{{- j}\quad \beta_{m - 1}}}}}}^{2}.$

[0028] These sets of phase candidates are significantly reduced innumber compared with algorithm 200 since s<M and s^(N−1)<M^(N−1). When sis very small, the number of phase differential sequences to searchbecomes much smaller, which leads to significant complexity savings. Asan example, for s=2, N=4 and M=4, there will be eight (8) sets of phasedifferential sequences that will result. This is a much smaller subsetof the sixty-four (64) phase differential sequences shown in FIG. 5,which would be processed in a conventional MSDD algorithm, such asalgorithm 200.

[0029] In step 304, the maximum resulting vectors from step 303determine the optimum phase differential sequence {β₁, β₂, . . . ,β_(N−1)} Steps 303 and 304 in combination can be expressed by thefollowing decision statistic: $\begin{matrix}{\eta^{new} = {\max\limits_{{\beta_{1} \in \quad P_{1}},\quad \ldots \quad,{\beta_{N - 1} \in P_{N - 1}}}{{r_{1} + {\sum\limits_{m = 2}^{N}{r_{m}^{{- j}\quad \beta_{m - 1}}}}}}^{2}}} & {{Eq}.\quad (6)}\end{matrix}$

[0030] When s=M, the statistic is simply η^(new)=η.

[0031] In step 305, the final information phase sequence {Δ{circumflexover (φ)}₁, Δ{circumflex over (φ)}₂, . . . , Δ{circumflex over(φ)}_(N−1)} is estimated from the optimum phase differential sequence{β₁, β₂, . . . β_(N−1)} using Equation (7) and the phase informationbits are obtained by Gray de-mapping. $\begin{matrix}{\beta_{m} = {\sum\limits_{k = 1}^{m}{\Delta \quad {\hat{\varphi}}_{k}}}} & {{Eq}.\quad (7)}\end{matrix}$

[0032]FIG. 4 shows a block diagram of MSDD parallel implementation 400,where N=4, s=2. Since N=4, there are N−1=3 parallel selection circuits401, 402, 403, for determining s^(N−1) (i.e., 8) subsets (P₁, P₂, P₃) ofcandidate phases. Selection circuit 401 comprises delay blocks 410, 411;conjugator 412, multiplier 413, multiplier 415 _(k) (k=0 to N−1),amplitude blocks 416 _(k) (k=0 to N−1), decision block 417 multipliers418, 419 and switch 450. Input symbol r_(k+3) passes through delays 410,411 for establishing r_(k) as the reference symbol and r_(k+1) as theconsecutive symbol against which the phase differential is to beestimated. The output of conjugator 412 produces conjugate r_(k)*, whichwhen multiplied with consecutive symbol r_(k+1) by multiplier 413,produces a phase difference value. Next, the phase difference ismultiplied by multipliers 415 _(k) to each phase in the set β_(k), whereβ_(k)=(2 πk/M, k=0, 1, . . . , M−1). Next, the products are passedthrough amplitude blocks 415 _(k) and input to decision block 417, whichselects the maximum s=2 inputs for the subset P₁=[β_(k1), β_(k2)]. Theoutputs of block 401 are the products r_(k+1) e^(−jβk1) and r_(k+1)e^(−jβk2) output by multipliers 418, 419.

[0033] Decision circuits 402 and 403 comprise parallel sets of similarelements as described for block 401. Decision circuit 402 includes delayblocks 420, 421, which allow processing of reference symbol r_(k) withr_(k+2), whereby decision block 427 chooses candidate phases P₂=[β_(k3),β_(k4)]. Likewise, block 403 includes delay block 431 to allow decisionblock 437 to select phase differential candidates P₃=[β_(k5), β_(k6)]for reference symbol r_(k) and symbol r_(k+3). Summer 404 addsalternating combinations of outputs from blocks 401, 402 and 403alternated by switches 450, 451, 452, respectively, plus referencesymbol r_(k). Since s=2, there are 2 ³=8 combinations of phasedifferential sequence (P₁, P₂, P₃) produced by switches 450, 451, 452.Decision block 405 selects the optimum phase differential sequence {β₁,β₂, β₃}, which is the phase differential sequence (P₁, P₂, P₃) thatproduces the maximum sum.

[0034]FIG. 6 shows the symbol error rate (SER) performance of the MSDDalgorithm for 16 PSK, where s=2 for different symbol observation lengthsN=3, 4 and 5. As shown in FIG. 6, reduced-complexity MSDD algorithm 300with s=2 provides almost the same performance as the original MSDDalgorithm 200 where s=M. This is because the MSDD algorithm 300 selectsone of the two closest phases between the vector r_(k+1)e^(−jβ) ^(_(k))1≦k≦N−1) and r₁ in order to maximize the statistic of Equation (6).Therefore, for 2<s<M, the performance is essentially the same as fors=2, which means there is no benefit to increasing the complexity ofalgorithm 300 to s>2. Therefore, the optimum results are gained usingthe simplest possible choice for s, that is s=2.

[0035] Table 1 shows the complexity comparison of algorithm 300 with s=2for symbol observation length N=5 against algorithm 200. The number ofphase differential sequences to search is reduced significantly,resulting in faster processing speeds. TABLE 1 No. of No. of phase phasedifferential differential sequences sequences Speed to search to searchfactor for MSDD 200 for MSDD 300 Reduction (x times M Modulation(M^(N−1)) (s^(N−1)) factor faster) 4  4 PSK 256 16 16 12 8  8 PSK 409616 256 229 16 16 PSK 65536 16 4096 3667

What is claimed is:
 1. A method for multiple-symbol differentialdetection phase evaluation of MPSK communication data comprising thesteps: a) observing a received set of N sequential symbols r₁ to r_(N),each pair of consecutive symbols having a phase differential from amongM phases where M>2; b) evaluating the set of symbols r₁, to r_(N) basedon selected sequences of N−1 elements that represent possible sequencesof phase differentials selected from the set (2 πk/M, k=0, 1, . . . ,M−1); and c) selecting S^(N−1) phase sequences of the form (P_(2i),P_(3i), . . . P_(Ni)) for i=1 to S for evaluating said symbol set, where1<S<M.
 2. The method of claim 1 wherein evaluating in step (b) furtherincludes estimating a phase differential between the first symbol r₁ andeach other symbol r_(k) (k=2 to N); wherein selecting in step (c)further includes selecting S closest phases β_(k1) to β_(ks) of the Mphases for each k, selected from the set (2 πk/M, k=0, 1, . . . , M−1),which produce the S largest values using the expression|r₁+r_(k+1)e^(−jβ) ^(_(k)) |², resulting in N−1 sets of S phasedifferentials; and the method further comprising: d) determining theoptimum phase differential sequence (β₁, β₂, . . . β_(N−1)) byattempting the S_(N−1) phase sequences from step (c) in the expression${{r_{1} + {\sum\limits_{m = 2}^{N}{r_{m}^{{- j}\quad \beta_{m - 1}}}}}}^{2}$

and choosing the phase sequence that produces the maximum result.
 3. Themethod of claim 2, further comprising: e) determining an estimate of atransmitted information phase differential sequence from the optimumphase differential sequence of step (d); and f) determining phaseinformation bits by Gray de-mapping.
 4. The method of claim 3, whereinstep (e) further comprises: calculating the estimate using therelationship$\beta_{m} = {\sum\limits_{k = 1}^{m}{\Delta \quad {\hat{\varphi}}_{k}}}$

where β_(m) (m=1 to N−1) represents the optimum phase differentialsequence of step (d) and Δ{circumflex over (φ)}_(k) represents estimatedthe transmitted information phase differential sequence.
 5. The methodof claim 2, wherein S=2 and the two closest phases are determined. 6.The method of claim 2, wherein M=4, N=4 and S=2, said phases β_(k1) toβ_(ks) are selected from the set (0, π/2, π, 3π/2), to produce S^(N−1)phase sets: (P₂₁, P₃₁, P₄₁) (P₂₁, P₃₁, P₄₂) (P₂₁, P₃₂, P₄₁) (P₂₁, P₃₂,P₄₂) (P₂₂, P₃₁, P₄₁) (P₂₂, P₃₁, P₄₂) (P₂₂, P₃₂, P₄₁) (P₂₂, P₃₂, P₄₂) 7.A system for performing multiple-symbol differential detection in acommunication receiver for a received set of N sequential r_(k) symbols(r₁ to r_(N)), each pair of consecutive symbols having a phasedifferential from among M phases where M >2, comprising: N−1 parallelselection circuits, each for producing a set of S candidate phases fromthe set (β_(k)=2 πk/M, k=0, 1, . . . , M−1), where 1<S<M, each selectioncircuit comprising: delay elements for allowing evaluation of thesequential symbols; M multipliers for producing parallel products(r_(k))(e^(−jβk)); a decision element for choosing S candidate phaseswhich produce the S maximum values within the expression|r₁+r_(k+1)e^(−jβk)|²; and S multipliers for producing the products(r_(k+i))(e^(−jβ′k)), where (i=1 to N−1) and β′_(k) represents one of Sselected phase candidates; a summer for adding the product outputs ofthe N−1 selection circuits; and a decision element for evaluating theS^(N−1) phase sequences from the N−1 parallel selection circuits andselecting the phase sequence which produces the maximum product value.